• Title/Summary/Keyword: Moment Formulation

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Numerical Formulation of Axisymmetric Shell Element and Its Application to Geotechnical Problems (축대칭 쉘 요소의 유한요소 수식화와 지반공학적 활용)

  • Shin, Hosung;Kim, Jin-Wook
    • Journal of the Korean Geotechnical Society
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    • v.36 no.12
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    • pp.27-34
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    • 2020
  • Use of axisymmetric shell element for the structure increases the efficiency and accuracy in finite element analysis of the interaction between the ground and the structure. This paper derived the force balance equation and the moment balance equation for an axisymmetric shell element based on Kirchhoff's theory. The governing equation for the axial deformation used the isoparametric shape function in the Galerkin formulation, and the governing equation for the shell bending used the higher-order shape function. The developed axisymmetric shell element was combined with Geo-COUS, a geotechnical finite element program for the coupled analysis with the ground. The accuracy of the developed element was confirmed through the example analyses of the circular plate and the liquid storage tank. And the energy balance equation for the axisymmetric shell element is presented.

Solving design optimization problems via hunting search algorithm with Levy flights

  • Dogan, Erkan
    • Structural Engineering and Mechanics
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    • v.52 no.2
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    • pp.351-368
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    • 2014
  • This study presents a hunting search based optimum design algorithm for engineering optimization problems. Hunting search algorithm is an optimum design method inspired by group hunting of animals such as wolves, lions, and dolphins. Each of these hunters employs hunting in a different way. However, they are common in that all of them search for a prey in a group. Hunters encircle the prey and the ring of siege is tightened gradually until it is caught. Hunting search algorithm is employed for the automation of optimum design process, during which the design variables are selected for the minimum objective function value controlled by the design restrictions. Three different examples, namely welded beam, cellular beam and moment resisting steel frame are selected as numerical design problems and solved for the optimum solution. Each example differs in the following ways: Unlike welded beam design problem having continuous design variables, steel frame and cellular beam design problems include discrete design variables. Moreover, while the cellular beam is designed under the provisions of BS 5960, LRFD-AISC (Load and Resistant Factor Design-American Institute of Steel Construction) is considered for the formulation of moment resisting steel frame. Levy Flights is adapted to the simple hunting search algorithm for better search. For comparison, same design examples are also solved by using some other well-known search methods in the literature. Results reveal that hunting search shows good performance in finding optimum solutions for each design problem.

Structural analysis of cracked R.C. members subjected to sustained loads and imposed deformations

  • Mola, F.;Gatti, M.C.;Meda, G.
    • Structural Engineering and Mechanics
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    • v.11 no.6
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    • pp.637-650
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    • 2001
  • A structural analysis of cracked R.C. members under instantaneous or sustained loads and imposed displacements is presented. In the first part of the paper the problem of deriving feasible moment-curvature diagrams for a long term analysis of R.C. sections is approached in an exact way by using the Reduced Relaxation Function Method in state I uncracked and the method suggested by CEB in state II cracked. In both states the analysis of the main parameters governing the problem has shown that it is possible to describe the concrete creep behaviour in an approximate way by using the algebraic formulation connected to the Effective Modulus Method. In this way the calculations become quite simple and can be applied in design practice without introducing significant errors. Referring to continuous beams, the structural analysis is then approached in a general way, applying the Force Method and the Principle of Virtual Works. Finally, considering single members, the structural analysis is performed by means of a graphical procedure based on the application of feasible moment-rotation diagrams which allow to easily solve various structural problems and to point out the most interesting aspects of the long term behaviour of cracked R.C. members with rigid or elastically deformable redundant restraints.

Experimental behaviour of composite beams subjected to a hogging moment

  • Pecce, Marisa;Rossi, Fernando;Bibbo, Fabio Antonio;Ceroni, Francesca
    • Steel and Composite Structures
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    • v.12 no.5
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    • pp.395-412
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    • 2012
  • The present work addresses the rotational capacity of steel-concrete composite beams, which is a key issue for the seismic design of composite frames. Several experimental tests from the literature are summarised, and the effects of various parameters on the available plastic rotation are discussed. Furthermore, a number of remarks are made regarding the need for supplementary experimental results. The authors carried out experimental tests on four composite beams in which the type, width and connection degree of the slab were varied. During the tests, the deflection and strains in the steel profiles and bars were measured and recorded, wherein the observed trends in the measured parameters indicated that the failure mode of the beam was influenced by global and local buckling. A comparison of the experimental results to the theoretical ultimate strengths and moment-curvature relationships confirms that buckling phenomena occurred after section yielding, even if a consistent plastic rotation developed. This rotational capacity is well evaluated by a formulation that is available in the literature.

Non-Prismatic Beam Element for Nonlinear Seismic Analysis of Steel Moment Frames II: Verification of Model (강재 모멘트 골조의 비선형 지진 해석을 위한 부등단면 보 요소 II: 모델의 검증)

  • Hwang, Byoung-Kuk;Cheon, Chung-Ha;Kim, Kee-Dong;Ko, Man-Gi
    • Journal of the Korean Society of Hazard Mitigation
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    • v.7 no.5
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    • pp.37-46
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    • 2007
  • This is the second of two companion papers that describe non-prismatic beam element for nonlinear seismic analysis of steel moment frames. Described in a companion paper is the formulation of a non-prismatic beam element to model the elastic and inelastic behavior of steel beams, which have reduced beam sections(RBS). This study describes the determination of yield surfaces, stiffness parameters, and hardening (or softening) rule parameters for RBS beam element. Analytical results of the RBS beam element show good correlation with test data and Finite Element Method(FEM) results.

Non-Prismatic Beam Element for Nonlinear Seismic Analysis of Steel Moment Frames I: Element Formulation (강재 모멘트 골조의 비선형 지진 해석을 위한 부등단면 보 요소 I: 요소개발)

  • Hwang, Byoung-Kuk;Jeon, Seong-Min;Kim, Kee-Dong;Ko, Man-Gi
    • Journal of the Korean Society of Hazard Mitigation
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    • v.7 no.5
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    • pp.27-35
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    • 2007
  • This study presents a non -prismatic beam element for modeling the elastic and inelastic behavior of the steel beam, which has the post-Northridge connections in steel moment frames that are subjected to earthquake ground motions. The elastic stiffness matrix for non-prismatic members with reduced beam section (RES) connection is in the closed-form. The plasticity model is of a discrete type and is composed of a series of nonlinear hinges connected by rigid links. The hardening rules can model the inelastic behavior for monotonic and random cyclic loading, and the effects of local buckling. Verification and calibration of the model are presented in a companion paper.

Dynamic Behavior Analysis of Reciprocating Compressor Pistons (왕복동형 압축기 피스톤의 동적 거동 해석)

  • 김태종
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.12 no.9
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    • pp.717-724
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    • 2002
  • In this study, a numerical analysis for the piston secondary dynamics of small refrigeration reciprocating compressors is performed. In general, the length of cylinder in this class of compressors is shortened to diminish the frictional losses of the piston-cylinder system. So, the contacting length between piston and cylinder wall is in variable with the rotating crank angle around the BDC of the reciprocating piston. In the problem formulation of the piston dynamics, the change in bearing length of the piston and all corresponding forces and moments are considered in order to determine the piston trajectory, velocity and acceleration at each step. A Newton-Raphson procedure was employed in solving the secondary dynamic equations of the piston. The developed computer program can be used to calculate the entire piston trajectory and the hydrodynamic force and moment as functions of crank angle under compressor running conditions. The results explored the effects of the radial clearance, lubricant viscosity, length of the cylinder wall, and pin location on the stability of the piston.

Investigating deformations of RC beams: experimental and analytical study

  • Parrotta, Javier Ezeberry;Peiretti, Hugo Corres;Gribniak, Viktor;Caldentey, Alejandro Perez
    • Computers and Concrete
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    • v.13 no.6
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    • pp.799-827
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    • 2014
  • In this paper, a theoretical and experimental study of the sectional behaviour of reinforced concrete beams subjected to short-term loads is carried out. The pure bending behaviour is analysed with moment-curvature diagrams. Thus, the experimental results obtained from 24 beams tested by the authors and reported in literature are compared with theoretical results obtained from a layered model, which combines the material parameters defined in Model Code 2010 with some of the most recognized tensions-tiffening models. Although the tests were carried out for short-term loads, the analysis demonstrates that rheological effects can be important and must be accounted to understand the experimental results. Another important conclusion for the beams tested in this work is that the method proposed by EC-2 tends to underestimate the tension-stiffening effects, leading to inaccuracies in the estimations of deflections. Thus, the actual formulation is analysed and a simple modification is proposed. The idea is the separation of the deflection prediction in two parts: one for short-term loads and other for rheological effects (shrinkage). The results obtained are in fairly good agreement with the experimental results, showing the feasibility of the proposed modification.

Study on Prediction and Control of Wind-Induced Heel Motion of Cruise Ship (바람 하중에 의한 크루즈선의 횡경사 예측 및 제어에 관한 연구)

  • Kim, Jae-Han;Kim, Yonghwan;Kim, Yong-Soo
    • Journal of the Society of Naval Architects of Korea
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    • v.50 no.4
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    • pp.206-216
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    • 2013
  • The present study considers the prediction of wind-induced heel of cruise ship and its stabilization. Wind load in ocean exerts on the surface of superstructure of cruise ship, which causes the heel moment on the ship. The calculation of wind load starts from choosing wind speed profile, so that the logarithmic wind profile model is applied in this study. Heel moment by wind load is calculated by adopting approximate formulation and applied to the ship motion analysis in time domain. Motion stabilizers, such as stabilizing fin and U-tube tank, are considered to reduce the heel effect as well as excessive roll motion. From this study, it is expected that the present method can be applied to the prediction and stabilization of the heel motion of cruise ships.

Steel fibre reinforced concrete for elements failing in bending and in shear

  • Barros, Joaquim A.O.;Lourenco, Lucio A.P.;Soltanzadeh, Fatemeh;Taheri, Mahsa
    • Advances in concrete construction
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    • v.1 no.1
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    • pp.1-27
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    • 2013
  • Discrete steel fibres can increase significantly the bending and the shear resistance of concrete structural elements when Steel Fibre Reinforced Concrete (SFRC) is designed in such a way that fibre reinforcing mechanisms are optimized. To assess the fibre reinforcement effectiveness in shallow structural elements failing in bending and in shear, experimental and numerical research were performed. Uniaxial compression and bending tests were executed to derive the constitutive laws of the developed SFRC. Using a cross-section layered model and the material constitutive laws, the deformational behaviour of structural elements failing in bending was predicted from the moment-curvature relationship of the representative cross sections. To evaluate the influence of the percentage of fibres on the shear resistance of shallow structures, three point bending tests with shallow beams were performed. The applicability of the formulation proposed by RILEM TC 162-TDF for the prediction of the shear resistance of SFRC elements was evaluated. Inverse analysis was adopted to determine indirectly the values of the fracture mode I parameters of the developed SFRC. With these values, and using a softening diagram for modelling the crack shear softening behaviour, the response of the SFRC beams failing in shear was predicted.